{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:40:00Z","timestamp":1753890000641,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,9,1]],"date-time":"2017-09-01T00:00:00Z","timestamp":1504224000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jo\\'{o}nsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the &amp;quot;absolute&amp;quot; protomodular context and to obtain a hierarchy among S-protomodular categories.<\/jats:p>","DOI":"10.23638\/lmcs-13(3:18)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:47Z","timestamp":1743701327000},"source":"Crossref","is-referenced-by-count":0,"title":["On some categorical-algebraic conditions in S-protomodular categories"],"prefix":"10.23638","volume":"Volume 13, Issue 3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4199-7367","authenticated-orcid":false,"given":"Nelson","family":"Martins-Ferreira","sequence":"first","affiliation":[]},{"given":"Andrea","family":"Montoli","sequence":"additional","affiliation":[]},{"given":"Manuela","family":"Sobral","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,9,1]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1611.09148v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1611.09148v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:28:47Z","timestamp":1743701327000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,1]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(3:18)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1611.09148v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1611.09148v1","asserted-by":"subject"}],"has-review":[{"id-type":"uri","id":"https:\/\/zbmath.org\/6790155","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1611.09148","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1611.09148","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2017,9,1]]},"article-number":"2552"}}